In RP water or aquous buffer is in mobile phase with minimum 3-5% or more. And with regards to the imiscibility of Chloroform and Water this is the problem what will kill the column packing. Following the HPLC Solvent Guide of Paul Sadek to rinse the column with different solvents and at the end with Chloroform will take very long time and at the end it is cheaper to buy a new column.
Of course you have to carefully exclude water when using chloroform, but having water in the mobile phase is not a necessary prerequisite for RP-HPLC. I've seen methods with nonaqueous eluents (this is sometimes coined "NARP" - nonaqueous reversed phase). The methods I've seen used gradients of methanol and acetonitrile or THF, though, no chlorinated solvents.
So, using dichloromethane/methanol (there is no immiscibility between those two, if I recall correctly) on C18 might be a possibility when you're dealing with extremely hydrophobic analytes - I'd prefer using a less hydrophobic stationary phase with the usual RP-eluents

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